CN114021357A - Structure random fatigue life estimation method based on stress probability density method - Google Patents

Abstract

The invention discloses a structure random fatigue life estimation method based on a stress probability density method, which comprises the steps of firstly, respectively extracting positive stress and shear stress of a thin-wall structure in three directions of x, y and z in a space coordinate system under the action of random load; then acquiring the Von Mises stress of the thin-wall structure which obeys Weibull distribution, and solving the Von Mises stress component square process to obtain Weibull parameters m and eta; then, stress of non-Gauss process is obtained based on the condition of narrow-band random processPeak probability density function P_p(s); finally, based on Miner linear accumulated damage theory, combining with stress peak probability density function P of non-Gauss process_p(s) establishing a stochastic fatigue life estimation model to determine the fatigue life of the thin-walled structure. The invention is not only suitable for the narrow-band stress process, but also suitable for the broadband random stress process after broadband correction.

Description

Structure random fatigue life estimation method based on stress probability density method

Technical Field

The invention relates to the technical field of aircraft life assessment, in particular to a structural random fatigue life estimation method based on a stress probability density method.

Background

The thin-wall shell structures such as a flame tube of an aeroengine combustion chamber, a heat-insulating and vibration-proof screen of an afterburner, a skin of a space plane and the like bear complex mechanical force load, aerodynamic force load, thermal load and high-sound strong noise load during working. These loads are often multi-axial fatigue loads, which are random and under these loads will generate complex internal stresses that result in fatigue failure of the thin-walled shell structure.

The traditional random fatigue life estimation method firstly samples and circularly counts the stress time history born by a structure, and then carries out damage summation calculation according to Miner theory. In this way, the fatigue life estimation of a component can only be made by the designer with complete knowledge of the load time history experienced by the component, whereas it is difficult to obtain a detailed load time history of the dangerous points during the design phase of the product and the component. In addition, when the load time history of some dangerous positions of the structure cannot be realized, the fatigue life of the component cannot be estimated by adopting the traditional method.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a structural random fatigue life estimation method based on a stress probability density method.

In order to solve the technical problems, the technical scheme adopted by the invention is as follows: the method for estimating the structural random fatigue life based on the stress probability density method comprises the following steps:

step 1: under the action of random loads, respectively extracting positive stress and shear stress of the thin-wall structure in three directions of x, y and z in a space coordinate system;

step 2: under the action of random loads, acquiring Von Mises stress of the thin-wall structure, which is distributed according to Weibull, and solving the Von Mises stress component square process to obtain Weibull parameters m and eta;

the Von Mines stress is defined in three-dimensional space as:

wherein s is_vRepresents the Von Mines stress, s_x、s_y、s_zRespectively represents the positive stress in the x, y and z directions, s_xy、s_yz、s_xzRespectively representing the shear stress in the x direction, the y direction and the z direction;

and step 3: obtaining a stress peak probability density function P of a non-Gauss process based on the condition of a narrow-band random process_p(s) the procedure is as follows:

step 3.1: the response of the weak damping system is regarded as a narrow-band random process, and a stress peak probability density function P of a non-Gauss process is deduced_p(s) approximate expression:

wherein Γ () is a gamma function; s is the stress amplitude, which for the Von Mises stress process is the combination of the effective peak and the process standard deviation, i.e.:

s＝s_{is effective}+σ(s_v)＝s_v-E(s_v)+σ(s_v)

Wherein s is_vIs the Von Mises stress, s_{Is effective}Is the Von Mises stress effective peak, E(s)_v)、σ(s_v) Mean and standard deviation of Von Mises stress, respectively;

step 3.2: integrating the formula in the step 3.1 to obtain a peak probability density function P of the Von Mises stress process_p(s) is:

and 4, step 4: based on Miner linear accumulated damage theory, stress peak probability density function P of non-Gauss process is combined_p(s) establishing a random fatigue life estimation model to determine the fatigue life of the thin-wall structure, wherein the process is as follows:

step 4.1: for a narrow-band random process, a Basquin equation is used as a failure model for fatigue life estimation, and the fatigue life T under the narrow-band random process is determined by combining a stress peak probability density function according to a Miner linear accumulated damage theory, wherein the process is as follows:

step 4.1.1: according to the Miner linear accumulated damage theory, under the constant-amplitude stress load, the damage caused by n working cycles is as follows:

wherein the content of the first and second substances,

for linear cumulative damage rate, destruction occurs when the sum of the cyclic ratios equals 1; n is_iRepresenting the working cycle times of the thin-wall structure under the constant-amplitude stress load; n is a radical of_iRepresenting the fatigue life value of the thin-wall structure under the same stress amplitude load;

step 4.1.2: by peak probability density function P of stress course_p(s) represents the working cycle times of the thin-wall structure in the stress amplitude s and the fatigue life T, and the formula is as follows:

n_i＝n(s)＝E[M_T]·T·P_p(s)

step 4.1.3: the curve of the relation between the external stress amplitude level S and the standard sample fatigue life N is an S-N curve equation:

s^bN＝K

wherein b and K are material constants determined in an S-N curve of the material;

step 4.1.4: integrating the equations in step 4.1.2 and step 4.1.3 with step 4.1.1 to obtain an integral expression:

and deducing to obtain the fatigue life T under the narrow-band random process:

wherein, E [ M_T]Is the average incidence of stress cycling; p_p(s) is the peak probability density function of the stress process; k and b are material constants determined in the S-N curve of the material;

step 4.1.5: for narrow-band stochastic processes, E [ M ]_T]Equal to zero crossing rate E [0]And calculating the total cycle number when the thin-wall structure is damaged as follows:

N_T＝TE[0]

wherein N is_TThe total number of cycles for which the thin-walled structure is damaged.

Step 4.2: for the broadband random process, the fatigue life T is corrected according to a Wirsching model by combining the influence of the local peak value on the fatigue life of the thin-wall structure, and the fatigue life T suitable for the broadband random process is obtained₁The process is as follows:

step 4.2.1: the Wirsching model corrects the fatigue life according to different power spectral density shapes of stress response to obtain a life estimation formula suitable for broadband random vibration:

wherein, λ is correction factor, and ED is damage crossing rate;

step 4.2.2: for wideband random processes, E [ M ]_T]Equal to the rate of occurrence of stress peaks E P]Corrected total number of cycles N_T1Comprises the following steps:

wherein the correction factor

m is the negative reciprocal slope of the S-N curve of the material, and alpha is the irregularity factor.

Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:

1. the method for estimating the structural random fatigue life based on the stress probability density method only relates to the power spectral density statistical parameter of the load process, is only related to the frequency structure of system input and response, and does not relate to the random amplitude sequence of the load process. Therefore, in the design stage of the structure, even if the designer cannot obtain the detailed information of the load history in advance, the designer can predict the random fatigue life of the structure by only estimating the statistical parameters of the stress random process to be experienced by the structure in advance according to the past experience or statistical simulation and combining the existing fatigue design theory.

2. The method provided by the invention not only carries out fatigue life estimation, but also carries out broadband correction on the calculation result, so that the method provided by the invention is not only suitable for the narrow-band stress process, but also suitable for the broadband random stress process after the broadband correction.

Drawings

FIG. 1 is a flow chart of a method for estimating a structural random fatigue life based on a stress probability density method according to an embodiment of the present invention;

fig. 2 is a schematic diagram of each functional module in software development of the structure random fatigue life estimation method based on the stress probability density method in the embodiment of the present invention.

Detailed Description

The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.

As shown in fig. 1, the method for estimating the structural random fatigue life based on the stress probability density method in the present embodiment is as follows.

Step 1: under the action of random loads, respectively extracting positive stress and shear stress of the thin-wall structure in three directions of x, y and z in a space coordinate system;

step 2: under the action of random loads, acquiring Von Mises stress of the thin-wall structure, which is distributed according to Weibull, and solving the Von Mises stress component square process to obtain Weibull parameters m and eta;

the Von Mines stress is defined in three-dimensional space as:

wherein s is_vRepresents the Von Mines stress, s_x、s_y、s_zRespectively represents the positive stress in the x, y and z directions, s_xy、s_yz、s_xzRespectively representing the shear stress in the x direction, the y direction and the z direction;

according to the random variable numerical characteristic theorem and the formula, the method can obtain:

wherein the content of the first and second substances,

for the Von Mines stress squaring process

The average value of (a) of (b),

is the mean of the Von Mines stress component squared process, E(s)_x)、E(s_y) Is the mean of the Von Mines stress components,

for the Von Mines stress squaring process

The variance of (a) is determined,

is Von Mines variance of the squared course of the stress component, σ²(s_x) Variance of Von Mines stress component.

For the zero-mean Guass process, the random variable X obeys a mean of 0 and a variance of σ²Normal distribution of (1), i.e. X to N (0, σ)²) The method comprises the following steps:

in the formula, E (X)^k) Is the k-th power mean of the random variable X, (k-1)! | A (k-1) (k-3) … × 3 × 1

σ²(X²)＝E(X⁴)-[E(X²)]²＝2σ⁴

Wherein σ²(X²) Is the 2 nd power variance of a random variable X, E (X)²) Is the 2 nd power mean of the random variable X;

for the Von Mines stress process that follows the Weibull distribution, the Von Mines stress squaring process can be derived

Variance of (2)

Comprises the following steps:

where Γ () is a gamma function.

Through simultaneous solution of formulas, Weibull parameters m and m can be obtained.

And step 3: obtaining a stress peak probability density function P of a non-Gauss process based on the condition of a narrow-band random process_p(s) the procedure is as follows:

step 3.1: the response of the weak damping system is regarded as a narrow-band random process, and a stress peak probability density function P of a non-Gauss process is deduced_p(s) approximate expression:

wherein Γ () is a gamma function; s is the stress amplitude, which for the Von Mises stress process is the combination of the effective peak and the process standard deviation, i.e.:

s＝s_{is effective}+σ(s_v)＝s_v-E(s_v)+σ(s_v)

Wherein s is_vIs the Von Mises stress, s_{Is effective}Is the Von Mises stress effective peak, E(s)_v)、σ(s_v) Mean and standard deviation of Von Mises stress, respectively;

step 3.2: integrating the formula in the step 3.1 to obtain a peak probability density function P of the Von Mises stress process_p(s) is:

and 4, step 4: based on Miner linear accumulated damage theory, stress peak probability density function P of non-Gauss process is combined_p(s) establishing a random fatigue life estimation model to determine the fatigue life of the thin-wall structure, wherein the process is as follows:

step 4.1: for a narrow-band random process, a Basquin equation is used as a failure model for fatigue life estimation, and the fatigue life T under the narrow-band random process is determined by combining a stress peak probability density function according to a Miner linear accumulated damage theory, wherein the process is as follows:

step 4.1.1: according to the Miner linear accumulated damage theory, under the constant-amplitude stress load, the damage caused by n working cycles is as follows:

wherein the content of the first and second substances,

for linear cumulative damage rate, destruction occurs when the sum of the cyclic ratios equals 1; n is_iRepresenting the working cycle times of the thin-wall structure under the constant-amplitude stress load; n is a radical of_iRepresenting the fatigue life value of the thin-wall structure under the same stress amplitude load;

step 4.1.2: by peak probability density function P of stress course_p(s) represents the working cycle times of the thin-wall structure in the stress amplitude s and the fatigue life T, and the formula is as follows:

n_i＝n(s)＝E[M_T]·T·P_p(s)

step 4.1.3: the curve of the relation between the external stress amplitude level S and the standard sample fatigue life N is an S-N curve equation:

s^bN＝K

wherein b and K are material constants determined in an S-N curve of the material;

step 4.1.4: integrating the equations in step 4.1.2 and step 4.1.3 with step 4.1.1 to obtain an integral expression:

and deducing to obtain the fatigue life T under the narrow-band random process:

wherein, E [ M_T]Is the average incidence of stress cycling; p_p(s) is the peak probability density function of the stress process; k and b are material constants determined in the S-N curve of the material;

step 4.1.5: for narrow-band stochastic processes, E [ M ]_T]Equal to zero crossing rate E [0]And calculating the total cycle number when the thin-wall structure is damaged as follows:

N_T＝TE[0]

wherein N is_TThe total number of cycles for which the thin-walled structure is damaged.

Step 4.2: for the broadband random process, the fatigue life T is corrected according to a Wirsching model by combining the influence of the local peak value on the fatigue life of the thin-wall structure, and the fatigue life T suitable for the broadband random process is obtained₁The process is as follows:

step 4.2.1: the Wirsching model corrects the fatigue life according to different power spectral density shapes of stress response to obtain a life estimation formula suitable for broadband random vibration:

wherein, λ is correction factor, and ED is damage crossing rate;

step 4.2.2: for wideband random processes, E [ M ]_T]Equal to the rate of occurrence of stress peaks E P]Corrected total number of cycles N_T1Comprises the following steps:

wherein the correction factor

m is the negative reciprocal slope of the S-N curve of the material, and alpha is the irregularity factor.

In the embodiment, a structural random fatigue life estimation method based on a stress probability density method is also subjected to software development, wherein a structural schematic diagram of each functional module is shown in fig. 2, and the first functional module is used for stress data acquisition and Von Mines stress calculation; the function module is used for calculating process parameters; the function module is used for fatigue life prediction.

Claims (5)

1. A structure random fatigue life estimation method based on a stress probability density method is characterized by comprising the following steps:

step 1: under the action of random loads, respectively extracting positive stress and shear stress of the thin-wall structure in three directions of x, y and z in a space coordinate system;

step 2: under the action of random loads, acquiring Von Mises stress of the thin-wall structure, which is distributed according to Weibull, and solving the Von Mises stress component square process to obtain Weibull parameters m and eta;

the Von Mines stress is defined in three-dimensional space as:

wherein s is_vRepresents the Von Mines stress, s_x、s_y、s_zRespectively represents the positive stress in the x, y and z directions, s_xy、s_yz、s_xzRespectively representing the shear stress in the x direction, the y direction and the z direction;

and step 3: obtaining a stress peak probability density function P of a non-Gauss process based on the condition of a narrow-band random process_p(s)；

And 4, step 4: based on Miner linear accumulated damage theory, stress peak probability density function P of non-Gauss process is combined_p(s) establishing a stochastic fatigue life estimation model to determine the fatigue life of the thin-walled structure.

2. The method for estimating the structural random fatigue life based on the stress probability density method as claimed in claim 1, wherein: the process of the step 3 is as follows:

step 3.1: the response of the weak damping system is regarded as a narrow-band random process, and a stress peak probability density function P of a non-Gauss process is deduced_p(s) approximate expression:

wherein Γ () is a gamma function; s is the stress amplitude, which for the Von Mises stress process is the combination of the effective peak and the process standard deviation, i.e.:

s＝s_{is effective}+σ(s_v)＝s_v-E(s_v)+σ(s_v)

Wherein s is_vIs the Von Mises stress, s_{Is effective}Is the Von Mises stress effective peak, E(s)_v)、σ(s_v) Mean and standard deviation of Von Mises stress, respectively;

step 3.2: integrating the formula in the step 3.1 to obtain a peak probability density function P of the Von Mises stress process_p(s) is:

3. the method for estimating the structural random fatigue life based on the stress probability density method as claimed in claim 1, wherein: the process of the step 4 is as follows:

step 4.1: for a narrow-band random process, a Basquin equation is used as a failure model for fatigue life estimation, and the fatigue life T in the narrow-band random process is determined according to a Miner linear accumulated damage theory and a stress peak probability density function;

step 4.2: for the broadband random process, the fatigue life T is corrected according to a Wirsching model by combining the influence of the local peak value on the fatigue life of the thin-wall structure, and the fatigue life T suitable for the broadband random process is obtained₁。

4. The method for estimating the structural random fatigue life based on the stress probability density method as claimed in claim 3, wherein: the process of step 4.1 is as follows:

step 4.1.1: according to the Miner linear accumulated damage theory, under the constant-amplitude stress load, the damage caused by n working cycles is as follows:

wherein the content of the first and second substances,

for linear cumulative damage rate, destruction occurs when the sum of the cyclic ratios equals 1; n is_iRepresenting the working cycle times of the thin-wall structure under the constant-amplitude stress load; n is a radical of_iRepresenting the fatigue life value of the thin-wall structure under the same stress amplitude load;

step 4.1.2: by peak probability density function P of stress course_p(s) represents the working cycle times of the thin-wall structure in the stress amplitude s and the fatigue life T, and the formula is as follows:

n_i＝n(s)＝E[M_T]·T·P_p(s)

step 4.1.3: the curve of the relation between the external stress amplitude level S and the standard sample fatigue life N is an S-N curve equation:

s^bN＝K

wherein b and K are material constants determined in an S-N curve of the material;

step 4.1.4: integrating the equations in step 4.1.2 and step 4.1.3 with step 4.1.1 to obtain an integral expression:

and deducing to obtain the fatigue life T under the narrow-band random process:

wherein, E [ M_T]Is the average incidence of stress cycling; p_p(s) is the peak probability density function of the stress process; k and b are material constants determined in the S-N curve of the material;

step 4.1.5: for narrow-band stochastic processes, E [ M ]_T]Equal to zero crossing rate E [0]And calculating the total cycle number when the thin-wall structure is damaged as follows:

N_T＝TE[0]

wherein N is_TIs of thin-walled structureTotal number of cycles when failure occurred.

5. The method for estimating the structural random fatigue life based on the stress probability density method as claimed in claim 4, wherein: the process of step 4.2 is as follows:

step 4.2.1: the Wirsching model corrects the fatigue life according to different power spectral density shapes of stress response to obtain a life estimation formula suitable for broadband random vibration:

wherein, λ is correction factor, and ED is damage crossing rate;

step 4.2.2: for wideband random processes, E [ M ]_T]Equal to the rate of occurrence of stress peaks E P]Corrected total number of cycles N_T1Comprises the following steps:

wherein the correction factor

m is the negative reciprocal slope of the S-N curve of the material, and alpha is the irregularity factor.

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